RATIONAL  DESIGN  OF  STEAM  HEADERS  AND  PIPING  SYSTEMS 


BY 


FRANK  MACKNET  VAN  DEVENTER 
B.  S.  University  of  Illinois,  1917 


THESIS 

Submitted  in  Partial  Fulfillment  of  the  Requirements  for  the 

Degree  of 

MECHANICAL  ENGINEER 

IN 

THE  GRADUATE  SCHOOL 

OF  THE 

UNIVERSITY  OF  ILLINOIS 

1922 


Digitized  by  the  Internet  Archive 
in  2017  with  funding  from 

University  of  Illinois  Urbana-Champaign  Alternates 


https://archive.org/details/rationaldesignofOOvand 


Pa^e  I 

RATIONAL  DESISU  OF  STEAi:  KEAPERS  ACT  PIPING  SYSTEIS. 

TABLE  OF  00I!TE1:TS. 

Page 


1 - Scope  and  Foreword.  ----------------------  i 

2 - Review  and  Criticism  of  I’ethods  Usually  Pollo\7ed  in  the 

Selection  of  Insulation.  ------------------  1 

3 - Proposed  Rational  I'ethod  for  the  Selection  of  Insulation.  - - - 2 

4 - Cost  Factors  Involved  in  the  Selection  of  Insulation.”  -----  2 

5 - Graphic  Method  of  Comparirig  Insulation  Charges.  - --  --  --  - 3 

6 - Fethods  Recommended  hy  Designers  and  Text  Book  V7r iters  for 

the  Proper  Pipe  Size  Determination.  ------------  3 

7 - Proposed  Rational  I'ethod  for  Selecting  Pipe  Sizes.  - --  --  --  4 

8 - Cost  Factors  Involved  in  the  Selection  of  Pipe  Sizes.  -----  4 

9 - Graphic  I.ethod  of  Comparing  Pipe  Size  Data.  - --  --  --  --  - 4 

APPENDIX  I. 

DESIGK  OF  A SIITLE  STEAI.'  HEADER. 

10  - Description.  -------------------------  6 

11  “ Steam  Conditions.  -----------------------  6 

12  - Load  Conditions.  ------------------------  6 

13  - Steam  Requirements.  -----------------------  6 

14  - Selection  of  Insulation.  --------------------  8 

15  - Analysis  of  Costs.  ----------------------  8 

16  - Explanation  of  Items  in  Table  Lo.  l.  --------------  8 

17  - Conclusions  on  Insulation.  ------------------  12 

18  - Selection  of  Header  Size.  -------------------  12 

19  - Explanation  of  Itemis  in  Table  ho.  2.  - --  --  --  --  --  --  12 

20  - Conclusions  on  Header  Size.  ------------------  16 

APPEKDIX  II. 

DESIGN  OF  A COITLICATED  STEAI:  HEADER. 

21  - Description.  --------------------------  18 

22  - Selection  of  Insulation.  -------------------  18 

23  - Load  Conditions.  ------------------------  18 

24  - Steam  Requirements.  ----------------------  18 

25  - Provision  for  Future  Extension.  ----------------  20 

26  - Selection  of  Header  Size.  -------------------  20 

27  - Explanation  of  Items  in  Table  No,  3.  --------------  20 

28  - Conclusions  on  Header  Size,  ------------------  26 

29  - Closing  Discussion  of  the  Rational  I'ethod.  - --  --  --  --  --  26 

APPEIH)IX  III. 

RADIATION  LOSSES  Ft^OF  BARE  AND  IFSTJLATED  PIPES. 28 


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APPEI^DIa  IV. 

THE  FLOW  OF  ST£A2f.  IE  PIPES. 


Page 


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31 

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34 

35 


The  Bahcock  Formula.  --------------------  33 

Standard  and  Extra  Strong  Pipes.  ---------------  33 

Superheated  Steam  ----------------------  35 

Exanple  of  Solution  by  the  Formula.  -------------  36 

G-raphic  Chart  for  the  Babcock  Formula.  - --  --  --  --  --  36 

Example  of  Graphical  Solution.  ----------------  38 


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Page  III 

LIST  OF  TABLES. 

Page. 


1 “ Selection  of  Steam  Pipe  Insulation,  -----------  9 

2 - Determination  of  Economical  Header  Size. 

(Simple  Header).  -------------------  13 

3 - Determination  of  Economical  Header  Size, 

(Complicated  Header).  ----------------  2I 

4 “ Pressure  Loss  Analysis,  -----------------  34 

5 - Hadiation  Loss  from  Bare  Pipe.  --------------  £9 

6 - Efficiency  of  Asbesto-Sponge-Pelted 

Sectional  Insulation.  ----------------  30 

7 - List  Prices  of  Pipe  Covering,  --------------  33 

8 - Factor  ”F’  for  the  Modified  Babcock  Pormula.  -------  34 

LIST  OF  FICURES. 

1 - Layout  of  a Simple  Steami  Header.  - --  --  --  --  --  - 7 

2 - Graphic  Study  of  Insulation  Thickness,  ----------  11 

3 - Graphic  Study  of  Header  Size  Determination, 

( S imple  Header 14 

4 - Layout  of  a Complicated  Steam  Header,  ----------  19 

5 - Graphic  Study  of  Header  Size  Detemlnation, 

(Complicated  Header).  ----------------  22 

6 - Graphic  Steami  Plow  Chart,  - --  --  --  --  --  --  --  - 37 

COHCLUSIOHS. 

Conclusions  on  Insulation,  ----------------  13 

Conclusions  on  Header  Size,  (Simiple  Layout)."  ------  ^6 

Conclusions  on  Header  Size.  (Complicated  Layout)."  - - - - 35 
Closing  Discussion  of  the  Rational  Method,  """"""""26 


Pa'^  1 

RATIOEAL  DESIGK  OF  STEAi:  HEADERS  m)  PIPING  STSTEKS 


1 - SCOPE  AKD  FOREWORD. 

The  scope  of  this  thesis  is  limited  to  that  part  of  design  which  deals  with 
(a)  the  selection  of  heat  insulating  coverings,  and  (b)  the  proper  pipe  sizes. 
The  remaining  two  points  to  be  considered  in  the  design  of  a steam  header,  name- 
ly, the  location  of  the  pipe,  and  provision  for  expansion,  are  thoroughly  treat- 
ed in  text  books  and  will  not  be  considered  herein. 

It  would  seem  at  the  outset  that  the  logical  order  of  treatment  would  be 
to  first  lay  out  the  piping  scheme  and  determine  the  proper  sizes.  Having  done 
so,  the  last  item,  would  be  to  determine  the  thickness  of  insulation  to  use  on 
the  pipe.  Under  the  "rational”  method  of  design,  however,  the  reverse  order 
becomes  better  suited  to  the  solution.  The  determination  of  pipe  size  involves 
the  amount  of  heat  radiated  from  the  system,  which  in  turn,  involves  the  thick- 
ness of  insulation.  Further,  it  is  good  practice  to  set  up  an  "insulation 
schedule"  which  indicates  the  economical  thickness  of  insulation  for  all  sizes 
of  pipe  which  may  occur  in  the  whole  plant.  By  drawing  up  this  schedule  first, 
the  proper  thicknesses  of  insulation  will  be  known  for  the  several  pipe  sizes 
considered  in  the  calculations  for  the  economical  pipe  size, 

2 - REVIEW  AM)  CRITICISE  OP  MITEODS  USUALLY  FOLLOWED  IE  THE 

selegtioe  of  IESULATION. 

Conversation  upon  the  subject  has  indicated  the  surprising  prevalence  of 
the  idea  among  designers  that  "a  little  insulation  does  some  good,  and  the  more 
the  better",  or,  as  one  designer  stated,  "Modern  plants  use  extreme  tempera- 
tures and  the  radiation  losses  become  enormous;  consequently,  too  much  insula- 
tion cannot  be  used" . 

The  fallaqy  of  this  idea  lies  in  the  fact  that  the  heat  saved  is  not  direct- 
ly proportional  to  the  thickness  of  the  insulation.  One  inch  of  insulation 
under  average  conditions  saves  about  89  per  cent,  of  the  heat,  which  would  be 
lost  from  the  bare  pipe.  Three  inches  saves  about  94  per  cent,  of  the  bare 
pipe  loss;  so  it  is  seen  that  the  last  two  inches  of  insulation,  which  costs 
about  two  times  as  much  as  the  first  inch,  is  only  5,6  per  cent,  as  effective 
in  saving  heat. 

The  Magnesia  Association  of  America  publishes  four  charts,  based  upon  four 
values  of  steam  cost,  each  chart  indicating  the  proper  thickness  of  65%  magne- 
sia to  use  for  each  pipe  size  and  for  various  temperature  differences.  The 
steam  costs  represented  by  the  four  charts  are:-  20^,  40^,  60^,  and  80^  per 
million  Btu.  When  steam  costs  do  not  coincide  with  one  of  these  four  values, 
the  result  must  be  obtained  by  observing  the  two  charts  for  lesser  and  greater 
steam  costs,  and  approximating  the  intermediate  value.  This  method  does  not 
permit  of  a satisfactorily  definite  solution.  A more  important  criticism  of 
these  charts,  is  the  fact  that  the  curves  are  regular  curves  without  inflec- 
tions. In  the  rational  method  of  analysis  it  will  be  found  that  these  cuirves 
are  not  regular,  due  to  the  fact  that  the  list  prices  for  various  thicknesses 
do  not  follow  a general  curve.  Hence  the  accuracy  of  such  charts  is  to  be 
doubted. 


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Page  E 

JoJms-J'anville,  in  their  bulletin  "Service  to  Power  Users",  publish  a 
brief  table  v/hich  indicates  the  ininirmmi  thickness  of  steam  pipe  insulation 
that  should  be  used  for  a given  character  of  service,  e.  g.  25  to  100  pounds 
steam  pressure,  100  to  200  pounds,  etc.  The  results  obtained  from  inter- 
polation in  this  table  are  questionable,  and  the  "minimunf’  thickness  does 
not  imply  "economical"  thickness  at  all, 

5 - PROPOSED  RATIOh^AL  liETHOD  FOR  SELEOTIKG  lESULATIOE, 

By  "Rational  method"  is  meant  that  Ciethod  which  effects  the  highest 
economiic  efficiency,  and  "highest  economic  efficiency"  means  the  lowest  total 
financial  charges  against  the  system  under  consideration.  The  rational 
method,  then,  consists  of  an  analysis  of  the  costs  against  the  system,  and 
the  determination  of  the  condition  which  corresponds  to  the  minimum,  value  of 
the  total  costs. 

4 - COST  FAGTORg  INVOLVED  IK  TFR  R-RTPHTION  OF  IKSULATIOl  . 

The  costs  which  are  chargeable  against  the  installation  are: 
a - Fixed  charges  - 

b ~ Interest  on  cost  of  insulation,  in  place  - 

c “ Effect  of  nature  of  naterial. 

d - Effect  of  thickness  of  material, 

e - Depreciation  of  covering, 

f “ Repairs  and  maintenance, 

g - Miscellaneous  (taxes,  insurance,  etc.) 

h “ Operating  charges  - 

i “ Cost  of  heat  radiated  - 

j ” Effect  of  natiore  of  material, 

k - Effect  of  thickness  of  material. 

EOTES: 

Item 

a Fixed  charges  include  those  which  continue  throughout  the  useful  life 
of  the  material,  whether  the  plant  operates  or  not. 

c Soma  materials,  having  higher  insulating  efficiency  than  others,  natural- 
ly corcnand  higher  prices,  and  the  interest  on  the  installation  irust 
correspond  to  the  first  cost, 

d Thick  coverings  naturally  are  more  costly  than  thin  coverings,  and  again 
higher  insulation  efficiency  is  accompanied  by  higher  interest  charges. 

h Operating  charges  are  those  i^diich  occur  only  when  the  plant  is  in  opera- 
tion. Most  plant  operating  charges  (e.  g.  fuel,  v/ater,  lubricants)  vary 
in  direct  proportion  v/ith  the  quantity  of  product  produced.  Radiation 
from  insulated  pipe,  however,  is  practically  a constant  amount,  regard- 
less of  the  rate  of  plant  operation, 

i,  .5  arid  k.  The  amount  of  heat  radiated  is  proportional  to  the  conplemient 
of  the  insulating  efficiency  of  the  covering.  The  efficiency  is  higher 


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Page  3 

for  some  materials  than  for  others,  and  increases  somewhat  with  thick- 
ness, 

5 - SriAPHIC  R:ETH0D  of  GOITARIKS  IKSULATIOK  GPJ.RGEg. 

The  manipulation  of  aata  for  the  preceding  outline  is  best  effected  by  a 
tabular  arrangement,  but  the  results,  costs,  are  most  easily  coir:pared  and 
analysed  by  a graphic  presentation.  Since  thickness  is  the  argument,  it  is 
plotted  as  abscissa.  Ordinates  are  costs,  and  three  cost  curves  may  be 
plotted  for  each  pipe  size; 

ll)  Annual  fixed  charges  on  insulation, 

(2)  Annual  cost  of  heat  radiated, 

(3)  Total  annual  cost. 

The  minimum  value  of  the  total  cost  curve  is  the  criterion  for  the 
economical  thickness  of  covering.  If  peculiar  inflections  occur  in  the  total 
cost  curve,  the  source  may  be  discovered  by  a glance  at  the  two  component 
curves , 

6 - l-ETHODS  REGOM'EKDED  BY  DESIGNERS  AEP  TEXT  BOOK  WRITERS 

FOR  PROPER  PIPE  SIZE  BETERFIMTIOK 


Two  general  methods  of  selecting  pipe  sizes  have  been  in  comm^on  use, 
namely,  the  velocity  method,  and  the  pressure  loss  method. 

The  velocity  method  consists  in  selecting  pipe  of  such  size  that  the 
velocity  of  the  steam  will  not  exceed  certain  values.  Undoubtedly  this  rule 
is  based  upon  the  theory  that  velocities  exceeding  the  prescribed  values  would 
result  in  excessive  pressure  loss  and  consequent  poor  economy. 

This  theory  is  only  partially  borne  out  in  practice.  Pressure  loss 
varies  as  the  square  of  the  velocity,  when  the  v/eight  of  steam  flowing  is  the 
variable,  and  it  is  found  that  for  velocities  mnach  in  excess  of  10,000  feet 
per  miinute  that  the  pressure  loss  per  100  feet  of  pipe  becomes  so  great  that 
it  is  excessive  for  long  runs  of  pipe.  But  the  average  steam  header  layout 
is  of  such  design  that  numerous  branch  connections,  at  which  steam  is  fed  into 
or  bleu  out  of  the  header,  effect  frequent  changes  of  velocity,  such  that  one 
or  m.ore  sections  of  the  header  may  contain  steam  at  almost  zero  velocity, 
while  another  section  may  carry  steam  at  an  extremely  high  velocity.  It 
would  not  be  proper  to  increase  the  size  of  the  section  which  carries  high 
velocity  steam*,  because  it  is  possible  that  a shifting  of  the  load,  by  re- 
placing one  or  more  of  the  operating  boilers  by  others  which  have  not  been  in 
operation,  may  almost  reverse  the  values  of  velocity  in  the  two  critical 
sections  mientioned.  For  this  reason,  it  is  aavisable  in  n.ost  cases  to  con- 
struct the  entire  heaaer  of  one  size  of  pipe,  and  it  is  seen  that  if  the  size 
were  so  selected  that  the  maximum  velocity  in  any  section  is  less  than  10,000 
feet  per  minute,  then  the  velocities  in  all  the  other  sections  woula  be  too 
lov/,  due  to  oversize  pipe,  resulting  in  excessive  superheat  loss,  or  condensa- 
tion, and  capital  charges. 

Further,  the  velocity  which  corresponds  to  the  miaximum  efficiency  in  one 
case  may  be  very  aifferent  from  that  in  another  case.  For  instance,  the 
relative  location  of  boilers  and  prim.e  movers,  as  ”back  to  back**,  ’’end  to  end'*. 


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Page  4 

etc,  has  a decided  effect  upon  the  characteristics  of  the  systea,  and  upon  the 
velocity  v/hich  corresponds  to  Ciaxijrum  econony. 

The  pressure  loss  method  consists  in  selecting  pipe  of  such  size  that  the 
pressure  loss  in  the  system  v/ill  not  exceed  certain  values.  The  principal 
difficulty  in  applying  this  method  is  in  knowing  v/hat  pressure  loss  corresponds 
to  maximum  economy.  Different  designers  recommend  from  five  to  20  pounds, 
and  occasionally  the  theory  is  advanced  that  a loss  of  50  pounds  or  more  is 
not  objectionable,  since  the  energy  remains  in  the  steam  as  additional  super- 
heat, The  latter  recomn.enaation  of  course  is  based  upon  a miis interpretation 
of  fact,  because  although  the  expansion  is  practically  a constant- total-heat 
process,  the  entropy  increases  during  the  expansion  and  the  percentage  of 
availability  of  the  energy  decreases,  so  that  less  is  available  for  conversion 
in  a prime  mjover,  and  more  nust  be  lost  in  the  exhaust. 

It  is  impossible  to  assign  a definite  value  for  the  velocity  or  pressure 
loss  v/hich  will  correspond  to  maximum  economy  in  ell  cases,  since  there  are  so 
many  factors,  such  as  type  of  header  laj^out,  type  of  prime  mover,  station  load 
factor,  etc  which  affect  the  problem. 

7 - PROPOSED  HATIOFAL  J^THOr  FOR  SELFTTIKG  PIPE  SIZES. 

’’Rational  J'ethod”,  as  previously  explained,  irc’icates  that  method  v;hich 
effects  the  lowest  total  financial  charges  against  the  system;  under  considera- 
tion. The  rational  method  of  determining  economical  pipe  size,  then,  consists 
in  analysing  the  costs  against  the  system  with  various  sizes  of  pipe,  and  find- 
ing the  size  which  corresponds  to  the  minimum:  value  of  total  costs, 

8 - GOST  FACTORS  mCLVED  IK  TEE  SELECT  I OK  OF  PIPE  SIZE. 

The  costs  which  are  chargeable  against  the  installation  are: 

Fixed  charges  - 

Interest  on  cost  of  pipe,  fittings,  and  insulation,  erecteu. 

Depreciation  of  pipe  and  insulation. 

Repairs  and  maintenance. 

Taxes  and  insurance. 

Operating  charges  - 

Annual  cost  of  steam  to  operate  prine  mover. 

Annual  cost  of  heat  radiated. 

9 - SRAPHIQ  1:ETHCD  OF  GOlTARlIIg  PIPE  SIZE  DATA. 

The  compilation  of  data  for  the  preceding  outline  is  best  effected  by  a 
tabular  arrangement,  but  the  variation  of  the  several  factors  which  affect  the 
costs,  as  well  as  the  costs  themselves,  are  most  easily  comi>ared  and  analyzed 
by  a graphic  presentation.  Since  pipe  size  is  the  argument,  it  is  plotted  as 
abscissa.  Ordinates  represent  oosts,  velocities,  etc,  to  suit  the  factors 
plotted.  The  following  items  may  be  shov/n  to  advantage: 

Steam  velocity 

Pressure  loss  due  to  friction 


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Page  5 


Pressure  loss  due  to  velocity  head. 

Total  pressure  loss. 

Water  rate  of  prime  mover. 

Annual  cost  of  steam  for  prime  mover. 

Annual  fixed  charges  on  pipe,  fittings,  and 
insulation. 

Annual  cost  of  heat  radiated. 

Total  annual  costs. 


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APPELTIX  I 


Page  6 
App,  I 


Design  of  a Siir.-ple  Stean  Header. 

The  plant  chosen  for  this  example  is  Boiler  Konse  ”1”  at  Rational  V/orks 
of  Kational  Tube  Company  at  FcKeesport,  Pennsylvania,  This  installation  was 
completed  and  placed  in  operation  in  Fay  1919, 

10  - DESCRIPTIOK.  (SeePig.  .1) 

The  plant  consists  of  one  - 10,000  kw.  (80^  power  factor)  Curtis  turbo- 
generator served  by  two  - 1471  horse  power  Babcock  and  V/ilcox  cross-drum 
boilers.  The  plant  is  located  in  a space  betv/een  tv/o  rolling  mills,  and  since 
there  is  no  rooir  for  future  extension,  additional  capacity  need  not  be  provided 
for  in  the  design  of  piping,  etc.  Also,  since  the  steam  conditions  differ 
from  those  enployed  in  the  general  miill  system,  the  plant  may  be  treated  as  an 
isolated  unit. 

11  - ST£A^;  COhDITIOhS, 

Eormal  gage  pressure  at  boiler  drum  - E50  lb,  per  sq,  in. 
Konnal  superheat  - 150°  P, 

TemiUerature  of  saturated  steam  - 406°  P, 

Temperature  of  superheated  steam  - 556°  P. 

Temperature  of  air  (assumed)  - 80®  P, 

12  - LOAD  COPDITIOFS, 

The  turbo-generator  is  intended  prinarily  to  serve  seven  motor-generator 
and  rotary  converter  sub-stations,  distributed  about  the  mill.  It  is  also 
connected,  through  transformers  and  a high-tension  transmission  sj'stem,  to 
other  power  generating  and  consuming  equipment  at  plants  of  other  subsidiary 
companies  of  the  United  States  Steel  Corporation,  In  designing  the  plant, 
it  v/as  anticipated  that  the  normal  load  on  the  generator  wox7ld  be  8000  kv/. , 
and  that  this  load  v/ould  be  carried  during  6400  hours  per  year.  During  the 
remaining  2360  hours,  when  the  rolling  miills  etc,  are  not  operating,  pov;er  may 
be  received  over  the  high  tension  system,  from  generating  stations  operating 
with  blast  furnace  gas  or  waste  heat  as  fuel. 

13  - STEAl^  REOUIHFITETS. 

The  water  rate  of  the  turbine  at  8000  kw,  output  is  12,9  lb.  per  kv;h. 
with  the  steam  conditions  enumjerated. 

With  the  steam,  required  for  auxiliaries  taken  from  the  end  of  the  header 
farthest  removed  from,  the  turbine,  the  only  load  which  need  be  considered  in 
the  design  of  the  header  proper  is  that  required  for  the  turbo-generator. 

At  the  design  load,  and  under  design  conditions,  the  steam  required  for 
the  turbine  = 8000  x 12.9  = 103,200  lbs.  per  hr. 


* KSt’S' 


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Pa<?^e  8 
App.  I 

14  - SRLEOTIOE  of  IKSULATIOK. 


Previous  studies  have  indicated  that  the  total  annual  charges  on  85^ 
IJagnesia  covering  are  about  four  percent  lower  than  on  Asbesto-Sponge-Felted; 
hence,  from  the  standpoint  of  cost  alone,  85^  I'agnesia  v/ould  be  re coirimended . 
Hov/ever,  Asbesto-Sponge-Felted  is  considered  more  durable,  more  easily  removed 
and  replaced,  and  less  liable  to  deterioration  from  de-hydration  at  steam  pipe 
temperatures.  These  advantages  cannot  easily  be  capitalized,  but  they  are 
considered  to  more  than  outweigh  the  four  percent  difference  in  annual  costs, 
and  Asbesto-Sponge-Felted  covering  will  be  used  in  this  analysis. 

15  - AITALYSIS  OF  COSTS. 

Table  Ko.  1 is  the  tabular  solution  of  economical  thickness  for  the  in- 
sulation. The  table,  together  with  the  explanatory  notes  which  follov/  it,  is 
self-explanatory. 

Fig.  2 is  a graphic  presentation  of  items  4,  6 and  7 in  the  table  and 
shows  the  trend  of  the  component  cost  lines,  as  well  as  the  deciding  factor, 
total  cost. 

16  - EXPLAKATIOE  OF  ITEI^P  IF  TABLE  W.  1. 

Item  1 . 


By  interpolation  and  extrapolation  frorni  Table  5, 
Appendix  III, 

Item  2 , 


With  13,500  Btu.  coal  at  ^3.50  per  net  ton  and  78%  boiler  efficiency, 
the  cost  of  heat  per  million  Btu.  at  the  boiler  nozzle  = 

1.000.000  X 3.50 


13,500  X 0.78  X 2000 


■ ;^0.166  per  miillion  Btu. 


Item  2 = Item  1 x 8760  x 0.166 

1,000,000 


0.001455  X Item  1. 


Item  3. 


By  interpolation  and  extrapolation  from  Table  6, 
Appendix  III. 

Itemi  4. 


Item  4 « Item  1 x (100  - item  3)  -r  100. 

Item  5. 

List  prices  from'  Table  7,  Appendix  III. 

Ket  prices  r list  less  30%  (quoted  January  19,  1922  by  H.  W.  Johns- 
I’anville  Go.) 

Iter  6. 

Item  6 r (item  5 + 60^  for  labor  and  accessories)  x 0.15  = 


H'^i«  M:, 


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Page  11 
App«  I 


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THICKINE55  OF  INSULATION. 


— Fig,  2.— 

Graphic  Study  of  Insulation  Thickme53. 


Pa^e  12 
App.  I 

s item  5 x 0,24, 

The  fixed  charges  are  assumed  to  be  : interest  6^,  depreciation  5^, 
repairs  and  maintenance  1^,  taxes,  insurance,  etc,  3^,  Total  15^, 

Item  7, 

Item  7 = item  4 + item  6, 

17  - COKOLUSIOES  OK  IKSULATIGK. 

The  curves  or  item  7 of  the  table  indicate  that  2 inches  is  the 
economical  thickness  for  all  sizes  from  10-inch  to  18-inch  pipe  inclusive, 
and  that  l-l/2  inches  is  the  most  economical  for  8-inch  pipe,  Hov;ever,  as 
the  difference  between  l-l/2  inches  and  2 inches  on  8- inch  pipe  is  only  four 
mills  x)er  year  per  foot,  it  is  considered  preferable  to  sim.plify  the  specifica- 
tion by  adopting  2 inches  as  the  thickness  for  the  six  sizes  of  pipe  considered. 

18  - SELEGTION  OF  HEADER  SIZE, 

Table  Ko.  2 is  the  tabular  solution  of  the  header  size  determination.  A 
comjplete  set  of  explanatory  notes  follows  the  table. 

Pig,  3 is  a graphic  presentation  of  the  im.portant  items  of  the  table.  The 
curves  are  numbered  to  correspond  v/ith  the  items  they  represent, 

19  - EXPLOv^ATIOK  OF  ITEI’F  ly  TABLE  W.  2, 

Item  1. 

From  quotation  submitted  by  Pittsburgh  Valve  Foundry  and  Construction  Go. 
I'arch,  1922. 

Item  2, 

From  quotation  submitted  by  H.  W.  Johns -l^anvi lie  Company  dated  February 
17,  1922. 

Item  3, 

Item  3 - 0,15  (item  1 + item  2).  The  fixed  charges  are  assumed  to  be: 
interest  6^,  depreciation  5%,  repairs  and  maintenance  1^,  taxes,  insurance, 
etc,  2%.  Total  15^. 

Item  4, 

Cost  of  heat  lost  r length  of  heaaer  (i,  e.  202  ft.)  x item  4,  column 
3 Table  1,  Appendix  I. 

Item  5, 

Use  formula  (2),  Appendix  IV. 
p = W2  L V F 

w = 103,200  4 60  = 1720  lb,  per  min. 

L r 165  ft.  (from  point  midway  betv;een  boilers). 


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App.  I 


V r 2.20 

F is  obtained  from  col.  6,  Table  8,  Appendix  lY. 
then: 

p r (1720)^  X 165  x 2.2  x P r 1.075  x 10®  x P. 
Item  6. 


Page  15 
App.  I 


Prom  "National  Pipe  Standards”,  table  p.  649,  col,  3. 


Item  7. 

Area,  sq.  ft.  ^ (item  6)^ 
Item  8. 

Velocity  (ft.  per  min.)  = 

1720  X 2.2  - S764 
area  item  7 


0.7854  , 

X = 0.00545  (item  6)^ 

144 

lb.  steam  per  min.  x sp.  vol, 
area  in  sq.  ft. 


Item  9. 

Velocity  head,  lb. 

( ft,  per  min. 

3600  X 2 X 32.2  x sp. 

Item  10. 


(ft.  per  sec.)^ 


per  sq.  in.  z 

sp,  vol,  X 144 


= ( item  8 

vol.  X 144  73,500,000 


The  pressure  loss  from  saturated  steam  dnjm  to  header,  including  dry 
pipe,  superheater,  non-return  valve,  feeder,  and  all  interrrediate  fittings 
is  7 lb,  per  sq,  in.  (Prom  test  data  on  similar  boiler,  corrected  to  the 
proper  rating) . 

Item  10  - item  5 + item  9+7. 

Item  11. 


Item  11  - 250  - item  10. 
Item  12, 


Btu.  per  hr.  «=  length  (202  ft.)  x item  1*  x (1  - 0,01  item  3*  ) 
•Ool.  3,  Table  1. 


Item  15. 

Total  heat  of  steam  at  boiler  nozzle  (265  lb,  per  sq.  in,  abs. 
and  150°  sux^erheat)  = 1290.4 

„ item  12 

Total  heat  of  steam  at  turbine  nozzle  z 1290.4  - - — 

lb.  steam  per  hr. 


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Page  16 
App.  I 

Item  14, 


Obtained  by  interpolation  from  F.  0.  Ellenwood’s  ’’Steam  Charts”, 
using  item  11  and  item  13  as  data. 

note  that  the  higher  superheat  for  small  pipes  than  for  large  pipes 
is  due  to  tv/o  causes:  (1)  less  radiation,  and  (2)  throttling  (expansion 
at  constant  total  heat),  and  that  for  8-inch  pipe  there  is  m.ore  superheat 
at  the  turbine  than  at  the  boiler,  even  though  the  total  heat  is  lower 
at  the  turbine  due  to  radiation. 


Item  15. 

The  water  rate  of  the  turbine  at  the  design  load  and  steam  conditions 
is  given  in  the  guarantee  as  12,9  lb,  per  kwh.  With  steam  at  250  lb, 
gage  and  150  deg.  superheat  (specifications)  the  electrical  energy  obtained 

from  one  pound  of  steam,  is  ^ . 264,50  Btu.  per  pound. 

12 « ^ 


A Study  of  the  pressure  corrections  used  by  the  Westinghouse  Electric 
and  J’fg,  Company  and  a check  calculation  by  thermodynamics  indicate  that 
the  loss  of  available  energy  amounts  to  0,25  Btu,  per  pound  of  steam,  for 
each  pound  decrease  of  pressure,  within  the  range  of  this  problemi. 

The  heat  lost  by  radiation  has  a airect  effect  by  reducing  the  available 
energy  per  pound  of  steam  by  an  amount  equal  to  the  total  Btu.  lost  by 
radiation  per  hour,  divided  by  the  total  weight  of  steam  flowing  per  hour. 

The  net  electrical  energy  available  per  pound  of  steam  then  is  264.50 
minus  the  losses  due  to  pressure  drop  ana  radiation,  and  the  corrected 
water  rate  of  the  turbine  is  equal  to  3412  divided  by  the  net  available 
energy  per  pound  of  steam. 

Item  16. 

Heat  carried  by  one  lb.  steam  from  fuel  to  turbine  nozzle  r 
item  13  - feed  water  tem,p.  (i.  e.  210°)  + 32  = item.  13  - 178. 

kw.  hr.  V/.  r.  Btu.  steam  Coal 

8000  X 6400  X item  15  x (item  13  - 178)  x 3,50 

Item  16  - - 

13,500  X 0.78  X 2000 

Coal  eff  ton 

8,51  X item  15  (item  13  - 178), 

Item  17, 

Item  17  = item  3 + item.  4 item  16. 

20  - COECLUSIOEF  OH  HEATHER  SIZE. 

An  inspection  of  the  total  cost  curve  of  Fig.  3 and  item  17  of  Table  Ko. 

2 indicates  that  a 12-inch  header  is  the  economical  size  to  install.  It  is 
noted  further  that  any  of  the  six  sizes  considered  would  involve  an  annual  loss 
of  less  than  .^800. 00  as  compared  v/ith  the  economical  size.  This  is  true  because 
the  disaavantages  of  increased  cost  and  increased  radiation  loss  for  the  larger 


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App,  I 

sizes  are  nearly  counterbalanced  by  the  advantage  of  less  pressure  loss.  It 
is  not  to  be  concluded,  however,  that  this  condition  occurs  in  all  cases  and 
that  any  size  within  a wide  range  will  constitute  an  economical  selection.  (See 
conclusions  at  end  of  Appendix  II). 


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App.  II 

APPmiX  II. 

DEE  IGF  OF  A aOlTLICATED  TTEAi:  HPADER. 


21  - DESGRIPTIOF.  (See  Fig.  4) 

The  plant  consists  of  four  15,000  kr;,  (80^  power  factor)  tiirho-generators 
served  by  eight  1500  hp,  "boilers,  A 1500  kw.  d.  c.  turho-generator , and  a 
Kotor-generator  set  receiving  power  froir  the  main  station  generators,  supply 
auxiliary  power,  the  tv;o  irachines  providing  a flexible  link  for  the  manipula- 
tion of  exhaust  steam  to  effect  a station  heat  balance.  One  turbine  driven 
feed  pump  and  steam  jet  air  exhausters  receive  steam  from  an  auxiliary  header 
located  under  the  main  header  under  the  generator  room.. 

22  - SELECT lOF  OF  IFSULATIOF. 


The  steam  conditions  are  the  same  as  in  Appenuix  I,  and  with  the  same 
coal  cost,  colorific  value,  and  boiler  efficiency,  the  insulation  specification 
v;ill  be  the  san,e,  viz.,  2-inches  of  Ashes to-Sponge-Fel tea  for  all  sizes.  (See 
par,  heading  #14ff,) 

23  - LOAD  GOIDITIOl.S. 

The  anticipated  loaa  is  an  industrial  load  consisting  of  several  steel 
miills  connected  electrically  by  a super-power  system..  The  normal  design  load 
is  45,000  kv/.  during  6400  hours  per  year. 

24  - STEAi:  REOUIHEI'.'EhTS. 


The  steam  requirements  for  the  plant  (excluaing  inteniiittent  denands  such 
as  soot-blowers,  ash  dumps,  etc.)  under  design  load  conditions  are: 


Item  EauiTanent 

a Fain  generators 

45,000  kw.  @ 12.75  lb. 

b Auxiliarj'  generator 

1200  kw.  C 30  lb. 

c Other  steam  auxiliaries 

Total 


Lb,  steam,  per  hr. 


573.750 

36.000 

20.000 

629.750 


The  main  generator  load  -would  be  normally  carried  on  three  machines,  but 
as  any  one  of  the  four  might  be  off  the  line,  it  is  assumed  for  design  purposes 
that  each  machine  carries  one  fourth  the  total  load.  Similarly,  seven  boilers 
would  normally  carry  the  load,  but  it  is  assumed  that  each  carries  one  eighth  of 
the  total  requirement.  The  actual  steam  distribution  in  the  header  system, 
would  be  different  for  each  possible  combination  of  units  in  service,  and  it  is 
quite  certain  that  the  assumptions  made  closely  represent  average  conditions. 

The  steam  required  by  each  turbine  = 

= 143,440  lb.  per  hr. 

4 


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Page  19 
App.  II 


— Fi6.  4 — 

— Layout  Of  a Complicated  5team  Header. 


Pa»e  20 
App.  II 

It  is  assumed  that  one-half  of  the  20,000  Ih,  per  hr.  used  by 
miscellaneous  auxiliaries  is  taken  from  each  end  of  the  main  header  under  the 
generator  room.  The  steam  distribution  in  the  header  is  discussed  under  item 
5,  par.  heading  # 27  . 

25  - PRCVISIOK  FOR  FUTURE  EXTEITPIOK. 

The  possibility  of  future  extension  must  not  be  overlooked.  In  a layout 
like  Figure  4,  however,  extension  may  be  disregarded,  since  additional 
generators  would  be  accompanied  by  additional  boilers,  and  the  piping  would  be 
extended  with  additional  cross-branches,  the  system  thus  expanding  similarly  to 
the  "Unit  System",  and  each  succeeding  unit  possessing  characteristics  similar 
to  the  original  unit. 

26  - SELECTION  OF  HEADER  SIZE. 

Table  l;o.  3 is  the  tabular  solution  of  the  header  size  problem,  A com- 
plete set  of  explanatory  notes  follows  the  table. 

Fig,  5 is  a graphic  presentation  of  the  important  item.s  of  the  table.  The 
curves  are  numbered  to  correspona  with  the  itemis  they  represent, 

A study  of  Fig.  5,  (or  Fig,  3)  is  enlightening.  It  is  noted  that  curve  17 
is  a "U"-curve.  Its  components  are  curves  3,  4,  and  16,  Curves  3 and  4 are 
increasing  functions,  i.  e.  they  increase  as  the  pipe  size  increases,  Hadiation 
increases  because  of  the  greater  amount  of  surface  exposea,  and  the  fixed 
charges  increase  because  of  the  higher  cost  of  materials.  Curve  16  is  a de- 
creasing function  because  the  v/ater  rate  of  the  generators  (curve  15)  decreases 
due  to  the  lesser  pressure  loss  in  large  pipes  (curve  10).  The  sum  of  an  in- 
creasing and  a decreasing  function  always  results  in  a "U" -curve,  which  must 
have  a minimum  value.  The  finding  of  this  minimum  value  by  analytical  con- 
siderations is  the  basis  of  the  "Rational"  method  of  design, 

27  - KXPLAI^ATIOK  OF  ITEi:S  IP  TABLE  ITO,  5, 

Item  1, 

From  quotation  submitted  by  the  Pittsburgh  Valve  Foundry  and  Con- 
struction Company,  Farch,  1S22.  (Correction  made  for  header  length). 

Item  2, 

From  quotation  submitted  by  H,  W.  Johns -Fanville  Company,  dated 
February  17,  1922,  (Correction  made  for  header  length). 

Item  3, 

Itemj  3 - 0,15  (item  1 + item.  2),  The  fixed  charges  are  asstuned  to 
be:  interest  6^,  depreciation  5^,  repairs  and  maintenance  1^,  taxes, 
insurance,  etc.  3^.  Total  15^, 

Item  4, 

Cost  of  heat  lost  = length  of  header  (i.  e.  632  ft.)  x item  4, 
colunn  3,  Table  1,  Appendix  I. 


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App,  II 


Page  23 
App.  II 

Item  5« 

In  order  to  determine  the  pressure  loss  in  a complicated  header,  it  is 
necessary  to  determine  the  distribution  of  steam  in  the  various  parts  of 
the  header.  Figure  4 and  Table  Ko.  4 demonstrate  the  method  of  calcula- 
tion. Each  section  of  the  header  is  given  a designating  letter,  which 
appears  in  column  1 of  the  table  (4). 

In  column  2 the  length  of  each  section  is  indicated. 

In  column  3 the  weight  of  steam^  flov/ing  in  each  section  is  listed. 

This  distribution  is  based  upon  the  assumiption  that  all  boilers  are  on  the 
line,  and  the  first  trial  assumes  that  the  three  cross  branches.  A,  B,  and 
G,  carry  equal  flov/.  The  flow  from  each  boiler  outlet  is  equal  to  the 
total  steamj  flow  divided  by  the  number  of  outlets,  - 

629,750  7 16  - 39,360  lb.  per  hr.  The  flow  in  each  of  the  cross  branches; 

629,750  . 3 - 209,920  lb.  per  hr.  Golumm  3 can  nov/  be  filled  in  by 
star  ting  *T/ith  any  convenient  branch,  as  A,  and  adding  or  subtracting,  as 
the  case  may  be,  as  steam  is  fed  into  or  bled  from]  the  header.  Column  4 
need  not  be  filled  in  unless  the  first  trial  is  found  to  be  satisfactory. 

Column  5 is  obtained  by  applying  the  formula  method,  as  in  item  5, 

Table  Eo.  2. 

Eov;,  if  the  steam  distribution  as  assinmed  is  correct,  the  system  will 
be  in  dynamic  equilibrium,  and  the  pressure  loss  betv/een  any  two  points, 
such  as  X and  Y,  figure  4 will  be  the  same,  whether  the  path  be  taken  via 
A,  B,  or  C. 

The  pressure  loss  from  X to  Y via  A for  14-inch  pipe  r 
D + A-I-E+I-Er  1.265  lb.  per  sq.  in.  Via  B = 

B + J ; 0.872  lb.  per  sq.  in.  Via  C =G+G+E+F+L+J-F-K= 
1.212.  Comparison  of  these  three  losses  shows  that  the  flow  through  B 
was  assumed  too  lov/  as  the  loss  by  that  route  is  lower  than  by  A or  C. 

The  average  of  these  losses  is  1.116  lb.  tier  sq.  in. 

Second  trial:  To  approximate  a corrected  flow  for  A,  B,  and  C,  the 

flow  in  each  of  these  branches  is  multiplied  by  the  square  root  of  1.116 
and  divided  by  the  square  root  of  the  first  trial  loss. 

Columns  6 and  6 constitute  the  second  trial.  The  calculation  is  the 
sanje  as  for  columns  3 and  5, 

The  loss  from  X to  Y with  the  values  tabulated  in  column  8 is:  via  A 
1.095,  via  B 1.075,  via  G 0.973.  The  average  is  1.048.  There  is  still 
som-e  variance  betv/een  these  values,  but  a third  trial  is  not  aavisable, 
since  there  is  a variation  betv/een  the  pressure  drops  to  the  various 
turbines  anjwvay,  hence  the  average  of  the  three  values,  or  1.048  is  taken 
as  the  drop  to  the  point  Y,  or  turbine  #2. 

Column  7 is  calculated  by: 

Vel.,  ft.  per  min.  = lb.  per  hr.  x sp.  vol.  3 0.0343  x Col.  6. 

60  X area,  sq.  ft. 


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Tafcle  No, 4 

Pressure  Loss  Analysis  of  Fig. 
For  14-Inch  Header. 


Second  Trial 

Pressure 

loss 

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Page  25 
App.  II 

Since  the  pressure  drop  to  turbine  #2  is  1.048  lb.  per  square  inch, 
the  drop  to  other  turbines  mavV  be  obtained  by  adding  or  subtracting  the 
losses  in  sections  between  the  tee  for  turbine  #2  and  the  tees  for  the 
other  turbines.  The  losses  to  the  various  turbines  are  found  to  be: 

#1  - 1.038,  #2  - 1.048,  #3  - 1.083,  #4  - 1.079.  The  average  is  1.062, 
which  is  entered  in  colunm  4 of  Table  Eo.  3 for  item  5.  The  xa*essure 
loss  for  the  other  sizes  is  calculated  by  multiplying  1,062  by  the  ratio 
of  the  respective  values  of  factor  P from  Table  Eo.  8,  Appendix  IV. 

Item  6. 

From  •’rational  Pipe  Standards”,  table  p.  649,  col.  3, 

Item  7. 

Area,  sq,  ft.  - (item  6)^ 


0.7854 

X 2 0,00545  (item  6)2 


144 


Item  8, 


Velocity  (ft.  per  min.)  in  interconnections.  A,  B,  and  C,  - 
lb.  steam  per  min,  x so,  vol.  r 9870  x 2.2  z 7.238 
Area  in  sq.  ft.  3 x area  item  7 


Item  9. 

Velocity  head,  lb,  per  sq.  in.  z 

( ft.  -per  min. )^ _ 

' 3600  X 2 X 32,2  x sp,  vol,  x 144 

Item  10. 


(ft.  per  sec. ) ^ 

2"g 

sp.  vol.  X '144 

( i tem  8 ) 2 
73,500,000 


The  pressure  less  from  saturated  steam  drum  to  hesuier,  including  dry 
pipe,  superheater,  non~retum  valve,  feeder,  and  all  intermediate  fittings 
is  7 lb.  per  sq.  in.  (From,  test  data  on  similar  boiler,  corrected  to  the 
proper  rating). 

Item  10  s item  5 + item  9+7, 

Item  11. 

Item  11  - 250  - item  10. 

Item  12. 

Btu,  per  hr.  z length  (632  ft.)  x item  1*  (1  - 0.01  item  3*). 

♦Col.  3,  Table  1. 

Item  13. 

Total  heat  of  steam  at  boiler  nozzle  (265  lb.  per  sq.  in.  Abs.  and 

150°  superheat)  z 1290.4  item  12 

Total  heat  of  steam  at  turbine  nozzle  z 1290.4  - 

lb,  steam  per  hr. 


Page  26 
App.  II 

Item  14. 


Obtained  by  interpolation  from  P.  0.  Ellenwood’s  **Steam  Charts”, 
using  item  11  and  item  13  as  data. 

Eote  that  the  higher  superheat  for  small  pipes  than  for  large  pipes 
is  due  to  two  causes:  (1)  less  radiation,  and  (2)  throttling  (ex- 
pansion at  constant  total  heat),  and  that  for  all  sizes  of  pipe  there  is 
more  superheat  at  the  turbine  than  at  the  boiler,  even  though  the  total 
heat  is  lov/er  at  the  turbine  due  to  radiation. 

Item  15. 


The  water  rate  of  the  turbine  at  the  design  load  and  steam  conditions 
is  given  in  the  guarantee  as  12.75  lb,  per  kwh.  With  steam  at  250  lb. 
gage  and  lOO  deg.  superheat  (specifications)  the  electrical  energy 
obtained  fror  one  pound  of  steam  Is  ^1^ 

12.75 


A study  of  the  pressure  corrections  used  by  the  Westinghouse  Electric 
and  llfg.  Company  and  a check  calculation  by  thermodj^'namics  indicate  that 
the  loss  of  available  energy  amounts  to  0.25  Btu.  per  pound  of  steam  for 
each  pound  decrease  of  pressure,  within  the  range  of  this  problem. 

The  heat  lost  by  radiation  has  a direct  effect  by  reducing  the  avail- 
able energj^  per  pound  of  steam  by  an  amount  equal  to  the  total  Btu.  lost 
by  radiation  per  hour,  divided  by  the  total  weight  of  steam  flov/ing  per 
hour. 


The  net  electrical  energy  available  per  pound  of  steam,  then,  is  268 
minus  the  losses  due  to  pressure  drop  and  radiation,  and  the  corrected 
v/ater  rate  of  the  turbine  is  equal  to  3412  divided  by  the  net  available 
energy  per  pound  of  steam. 

Item  16. 


Heat  carried  by  one  pound  of  steam  from  fuel  to  turbine  nozzle  - 
item  15  - feed  water  temp.  (i.  e.  210°)  + 32  = item  13  - 178. 

kw  hr.  w.  r.  Btu.  steam  Coal 

Item  16  - 45,000  x 6400  x item  15  x (item  13-178)  x 3.50 

13,500  X 0.78  X 2000 
Coal  eff.  ton 
47.9  X item  15  x (item  15  - 178). 


Item  17. 


Item  17  r item  3 + item  4 + item  16. 

28  - GOHCLUSIOES  OH  HEADER  SIZE. 


Inspection  of  the  total  cost  curve  of  Pig.  5 and  item  17  of  Table  Eo.  3 
indicates  that  a 14-inch  header  is  the  economical  size  to  install. 

29  - CLOSIEG  DISCUSSION  OF  THE  RATIONAL  IvETHOB. 

The  failure  of  the  velocity  method  is  proved  by  a comparison  of  Tables 


iWf- 


Pa^  27 
App.  II 

Fos.  2 and  3.  In  tatle  Ko.  2 it  is  found  that  the  velocity  corresponding  to 
the  economical  size  is  5000  ft.  per  min.  Kow,  if  the  second  design  problem 
(Table  Ko.  3)  were  solved  on  the  basis  of  5000  ft.  per  m.in.  velocity  in  the 
BAin  branches.  A,  B,  and  C,  a 17-inch  (0.  D.)  heavier  would  have  been  selected. 
Item  17  indicates  that  the  annual  charges  against  this  header  would  be  v350,00 
per  year  greater  than  those  against  the  14-inch.  Hence,  if  a designer’s  time 
is  required  for  one  month  (which  is  much  longer  than  should  be  required)  to 
make  a rational  analysis,  his  salary  v/ould  be  saved  in  fromj  one  to  two  years, 
which  is  considered  a good  investment.  Further,  in  col.  7 of  Table  Ho.  4 it 
is  found  that  velocities  in  the  14-inch  header  range  from  270  to  8060  ft.  per 
min.  Thus  the  velocity  method  loses  most  of  its  significance  at  once. 

It  is  interesting  to  note  that  the  total  pressure  loss  for  the  economical 
headers  in  the  tv/o  problems  are  8,16  and  8.68  lb.  per  sq.  in.  respectively.  It 
does  not  follow,  however,  that  8 to  9 lb.  m^ay  be  assumed  as  the  economical  drop 
for  all  cases.  Tv/o  exairples  v/ill  serve  to  point  out  the  fallacy  of  such  a 
conclusion,  (l)  There  are  ma,ny  factors  which  affect  the  probler  , one  of  which 
is  fuel  cost.  In  some  localities  fuel  costs  are  double  those  in  other 
localities,  and  v/here  the  cost  is  high,  larger  headers  are  warranted  since  the 
energy  lost  through  pressure  drop  has  a greater  value  than  with  lov;  fuel  cost. 
The  effect  of  high  fuel  cost  on  Fig,  5 is  to  raise  curve  16,  v/hich  tends  to 
shift  the  minimum  value  of  curve  17  towards  the  right,  (2)  It  is  obvious  that 
a greater  pressure  drop  is  warranted  in  a stand-by  plant  operating  with  a low 
yearly  load  factor  than  in  a high  load  factor  plant,  since  in  the  case  of  the 
former  the  financial  cost  of  an  "excessive”  pressure  drop  for  only  a few  hours 
a day  or  month  is  small,  and  the  high  fixed  charges  on  the  greater  cost  of  a 
large  header  are  not  warranted. 

A well  known  Central  Station  designer  has  criticised  the  rational  method, 
claim.ing  that  too  much  time  is  required,  that  a designer  who  is  ijroficient 
enough  to  do  such  v/ork  is  worth  much  more  on  other  phases  of  the  work,  and  that 
satisfactory  results  are  obtained  by  a good  guess  based  upon  experience.  This 
criticism  may  have  some  Justification,  but  it  is  the  author’s  firm  contention 
that  even  if  the  pressure  of  time  does  require  ”a  good  guess”  rather  than  com- 
plete analysis,  that  a much  m^ore  intelligent  guess  may  be  made  if  the  designer 
has  gone  through  at  least  one  complete  problem  by  the  rational  method,  which 
will  endow  him  v/ith  a knowledge  of  the  various  factors  affecting  the  problem, 
and  their  relative  importance. 

Further,  for  a designer  who  proposes  to  use  the  pressure  loss  method  of 
design,  the  additional  v/ork  required  to  complete  the  rational  method  is  not 
great,  and  it  will  undoubtedly  be  found  to  be  Justified. 

In  view  of  the  facts  brought  out  in  this  studj’’,  the  rational  method  is 
recommended  by  the  author  as  the  most  satisfactory  method  of  steam  header  de- 
sign. 


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Page  20 
App.  Ill 

APPEKDIX  III. 

HALIATIGIj  LOSSES  FEOF  BARE  APE  lESULATED  PIPES. 


Protably  the  most  reliable  experimental  data  available  on  radiation 
losses,  are  those  reported  by  Ej:.  L.  B.  Eclvlillan  in  Vol«  37  of  Trans.  A.S.E.E, 

Table  Eo.  5,  published  in  ” Johns-Eanville  Service  to  Power  Users”  is  based 
upon  EcEillan' s experimental  data,  and  is  considered  reliable.  The  tempera t\ire 
differences  at  the  column  headings  in  this  table  refer  to  those  between  outside 
pipe  surface  and  surrounding  air.  Analysis  of  Ecllillan’s  experiments  indicates 
that  with  zero  velocity  inside  the  pipe,  the  inner  surface  and  metal  resistance 
for  bare  pipes  is  about  1.27  percent  of  the  total  resistance  for  saturated 
steam,  and  9.45  percent  for  superheated  steam.  The  magnitude  of  the  inner 
surface  resistance  is  known  to  decrease  as  velocity  increases,  but  the  exact 
relation  between  these  two  quantities  is  not  known.  It  is  known,  however, 
from  tests  made  with  air,  that  a small  increase  in  velocity  is  accompanied  by  a 
large  decrease  in  surface  resistance.  It  may  therefore  be  concluded  that  at 
the  customary  high  velocities  in  steam  headers,  the  inner  surface  resistance  is 
less  than  one  or  tv'O  percent  of  the  total  resistance,  and  hence  sufficient 
accuracy  is  obtained  by  neglecting  the  resistances  imposed  by  the  inner  surface 
and  the  pipe  metal.  Table  Eo.  5 may  then  be  used  by  interpreting  the  column 
headings  as  "temperature  difference  between  steam  and  surrounding  air”. 

The  efficiency  of  an  insulating  covering  is  defined  as  the  ratio  of  the 
amount  of  heat  saved  by  using  the  insulation,  to  the  amount  v/hich  wou'ld  be 
lost  if  the  pipe  were  left  bare,  expressed  as  a percentage. 

To  determine  the  amount  of  heat  radiated  from  an  insulated  pipe,  then, 
it  is  necessary  to  determine  the  amount  radiated  from  a bare  pipe,  and  multiply 
this  loss  by  the  efficiency  of  the  insulation. 

The  efficiencies  of  comrercial  pipe  insulating  materials  vary  from  about 
50  percent  to  about  97  percent,  depending  upon  the  nature  of  the  material,  the 
thickness  of  the  insulation,  the  temperature  difference,  and  the  pipe  size. 

Table  Ko.  6 taken  from  ” Johns-Manville  Service  to  Pov/er  Users”  shows  the  ef- 
ficiencies of  Johns -Eanvi lie  "Asbesto-Sponge-Felted”  insulation. 

Table  Ko.  7,  from  " Johns-Eanville  Service  to  Power  Users”  gives  the  list 
prices  of  all  classes  of  pipe  coverings.  Discounts  vary  with  the  grade  of 
material  and  market  value. 


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Page  29 
App.  Ill 


TAPU  ITO.  5. 

RADI  AT  TOP  LOSg  BARE  PIPE. 


Total  Heat  Loss  in  B.  t.  u.  Per  Hour  Per  Lineal  Foot  of  Bare  Pipe  of  Different  Sizes  and 
Per  Square  Foot  of  Flat  Surfaces  and  at  Various  Temperature  Differences 

(For  finding  losses  at  temperatures  between  those  shown,  the  B.  t.  u.  Differences  per  Degree  are  given  in  small  type  between  the  Main  Columns) 
Area  of  Temperature  Differences 


Pipe  Sur-  50° 

100° 

150° 

200° 

250° 

300° 

350° 

400° 

450° 

500° 

Pipe 

Size 

lin.  ft 

Heat  Loss  m B.  t 

u.  per  lineal 

ft.  per  Hour 

K" 

.220 

21.5 

*.52 

47.3 

♦.64 

79.2 

*.76 

117.3 

*.go 

162.3 

*1.06 

215.2 

♦1.28 

279.1 

*1.52 

355.1 

*1.93 

451.4 

*2.37 

569.8 

H" 

.274 

26.8 

.64 

59.0 

.79 

98.6 

.96 

146.8 

1.11 

202.1 

1-33 

268.5 

I.S8 

347.6 

1.89 

442.2 

2.40 

562.2 

2.95 

709.7 

1" 

.344 

33.6 

.8i 

74.0 

1. 00 

123.8 

1. 19 

183.4 

I.4I 

253.7 

1.67 

337.4 

1.98 

436.5 

2.37 

555.2 

3-03 

705.4 

3-69 

891. 

IK" 

.435 

42.5 

1. 01 

93.6 

1.26 

156.6 

1. 51 

231.9 

1.78 

320.8 

2.09 

425.4 

2. S3 

551.9 

3.00 

702.1 

3.80 

892.6 

4.68 

1126.7 

IK" 

.498 

48.7 

1. 17 

107.2 

1.44 

179.3 

1.72 

265.4 

2.04 

367.3 

2.39 

487. 

2.90 

631.8 

3-44 

803.8 

4-36 

1021.9 

5.36 

1289.8 

2" 

.622 

60.9 

1.46 

133.9 

1.80 

223.9 

2.15 

331.5 

2.S4 

458.7 

2.99 

608.3 

3-62 

789.2 

4.29 

1003.9 

5-45 

1276.3 

6.69 

1611. 

2K" 

.753 

73.4 

1.76 

161.6 

2.18 

270.4 

2.60 

400.3 

3-07 

553.9 

3.61 

734.5 

4-37 

952.8 

S.19 

1212.1 

6.58 

1541.1 

8.08 

1945.1 

3" 

.917 

89.6 

2.15 

197.3 

2.66 

330.1 

3-17 

488.8 

3-75 

676.3 

4.41 

896.8 

5-33 

1163.4 

6.33 

1480. 

8.03 

1881.7 

9.87 

2375. 

3K" 

1.047 

102.3 

2.46 

225.3 

3.03 

376.9 

3.62 

558.1 

4.28 

772.2 

5.04 

1024. 

6.09 

1328.4 

7.23 

1689.9 

9.17 

2148.4 

II. 3 

2711.7 

4" 

1.178 

115.1 

2.77 

253.5 

3-41 

424.2 

4.07 

627.9 

4.82 

868.8 

5.67 

1152.1 

6.85 

1494.6 

8.13 

1901.3 

10.3 

2417.3 

12.7 

3051. 

4K" 

1.309 

127.9 

3-07 

281.5 

3.79 

4 70.9 

4-53 

697.2 

5-35 

964.7 

6.29 

1279.2 

7.61 

1659.5 

0.03 

2111.1 

11.05 

2684. 

14.1 

3387.7 

5" 

1.456 

142.2 

3.42 

313.1 

4.21 

523.8 

5-03 

775.5 

5-95 

1073. 

7.00 

1423. 

8.46 

1846. 

10. 0 

2348.4 

12.7 

2985.7 

15.7 

3768.5 

6" 

1.734 

169.4 

4-05 

371.9 

S.04 

623.9 

6.00 

923.7 

7.09 

1278.1 

8.34 

1694.9 

10. 1 

2198.7 

12.0 

2797.1 

15-2 

3556.2 

18.6 

4488.5 

7" 

2.00 

195.0 

4.71 

430.4 

5. 79 

720.0 

6.92 

1066.0 

8.10 

1475.6 

9.61 

1956. 

11.66 

2539. 

13.78 

3228. 

17.46 

4101. 

21.6 

5180. 

8" 

2.257 

220.6 

5.30 

485.7 

6.54 

812.5 

7.81 

1203. 

9.23 

1664.5 

10.8 

2207.3 

I3-I 

2863.6 

IS.6 

3642.8 

19.8 

4631.4 

24-3 

5845.6 

9" 

2.52 

246.0 

5.92 

542. 

7.30 

907. 

8.72 

1343. 

10.34 

1860. 

12. 1 

2465. 

14-7 

3200. 

17-4 

4070. 

22.0 

5170. 

27.2 

6530. 

10' 

2.817 

275.4 

6.62 

606.2 

8.16 

1014.1 

9-75 

1501.5 

II. 5 

2077.5 

13.6 

2755. 

16.4 

3574.1 

19.5 

4546.6 

24.7 

5780.5 

30.3 

7296. 

11' 

3.08 

300. 

7.26 

663. 

8.92 

1109. 

10.66 

1642. 

12.6 

2272. 

14.76 

3010. 

17.9 

3905. 

21.3 

4972. 

26.9 

6315. 

33.3 

7980. 

12" 

3.34 

326. 

7.86 

719. 

9.68 

1203. 

11.54 

1780. 

13.7 

2465. 

16.02 

3266. 

19-4 

4235. 

23.1 

5390. 

29.2 

6850. 

36.0 

8650. 

14'o.  d. 

3.66 

357. 

S-.SQ 

786. 

10.64 

1318. 

12.64 

1950. 

15-0 

2700. 

17.06 

3580. 

21.3 

4645. 

25-2 

5905. 

31.9 

7500. 

39.5 

9475. 

16"o. d. 

4.19 

408. 

9.84 

901. 

12.2 

1510. 

14-5 

2233. 

17.2 

3095. 

20.1 

4100. 

24.4 

5320. 

28.9 

6765. 

36.5 

8590. 

45.2 

10850. 

Flat, 

Heat  Loss  in 

B.  t. 

u.  per  sq.  ft. 

per  Hour 

Curved. 

or  \ . 

97.5  : 

2.3s 

215.2 

2.90 

360.0 

3.46 

533.0 

4.10 

737.8 

4.80 

978.0 

5.83  : 

1269.4 

6.89  1614.0  8.73  2050.6  10.8 

2590.0 

Cylindrical  1 

Heat  Loss  in 

B.  t. 

u.  per  sq.  ft.  per  degree  temperature  difference  per  Hour 

Surfaces 

1.950 

2.152 

2.400 

2.665 

2.951 

3.260 

3.627 

4.035 

4.557 

5.180 

♦Example  2"  Pipe,  235°  Temp.  Difference.  235°  — 200°  = 35°;  35°  x 2.54  (B.  t.  u.  per  degree)=88.9  B.  t.  u.  331.5-h88.9  = 420.4;  B.  t.  u.  loss 
at  235°  Temp,  difference. 


TABLE  rO.  6. 

EFFICIEKGY  OF  ASBESTO-SPOESE-FELTED 

SECTIOKAL  lESULATIOL. 


Page  30 
App.  Ill 


EfRciencies  of  Standard  Thick  Johns-Manville  Asbesto-Sponge  Felted  Sectional  Pipe 

Insulation  on  Various  Sizes  of  Pipes 

Temperature  Difference  Between  Steam  in  Pipe  and  Air  Surrounding  Pipe 


Pipe  Size, 
Inches 


H. 

M. 


IK. 
1 K- 
2 . 

2K. 

3 

3K. 

4 

4K. 

5 

6 

7 

8 
9 

10 


50° 

100° 

150° 

200° 

250° 

300° 

350° 

400° 

450° 

500 

Per  Cent  Efficiencies 

68.5% 

71.9 

71.2% 

74.3 

73.3% 

76.2 

75.5% 

78.1 

77.1% 

79.6 

78.7% 

81. 

80.4% 

82.6 

81.9% 

83.8 

83.1% 

85. 

84.5% 

86.2 

74.3 

76.5 

78.2 

79.9 

81.3 

82.6 

84. 

85.2 

86.2 

87.4 

75.7 

n.i 

79.5 

81. 

82.3 

83.5 

84.9 

86. 

86.9 

88. 

77 

79. 

80.5 

82. 

83.2 

84.4 

85.7 

86.7 

87.6 

88.6 

78.6 

80.4 

81.9 

83.3 

84.4 

85.5 

86.7 

87.6 

88.5 

89.3 

79.8 

81.5 

82.9 

84.3 

85.3 

86.3 

87.5 

88.4 

89.2 

90.3 

80.6 

82.2 

83.6 

84.9 

85.9 

86.8 

87.9 

88.8 

89.6 

90.3 

81.2 

82.8 

84.1 

85.4 

86.3 

87.3 

88.3 

89.2 

89.9 

90.6 

81.8 

83.3 

84.5 

85.8 

86.7 

87.6 

88.7 

89.5 

90.2 

90.9 

82.1 

83.6 

84.8 

86. 

87. 

87.9 

88.9 

89.7 

90.4 

91.1 

82.3 

83.8 

85. 

86.2 

87.1 

88. 

89. 

89.8 

90.5 

91.2 

82.7 

84.2 

85.4 

86.5 

87.4 

88.3 

89.3 

90.1 

90.7 

91.4 

83. 

84.5 

85.6 

86.8 

87.6 

88.5 

89.5 

90.2 

90.9 

91.6 

83.4 

84.8 

85.9 

87. 

87.9 

88.7 

89.7 

90.4 

91.1 

91.7 

83.5 

84.9 

86. 

87.2 

88. 

88.8 

89.8 

90.5 

91.2 

91.8 

83.8 

85.1 

86.2 

87.3 

88.2 

89. 

89.9 

90.6 

91.3 

91.9 

Johns- 

Manville  Asbesto-Sponge 

Felted 

Sectional  Pipe 

Insulation 

on  Various  Sizes  of  Pipe 


Pipe  Size, 
Inches 


K. 

1 

IK. 

IK- 

2 


2K 

3 

3H 

4 

4K 

5 

6 

7 

8 

9 . 
10 


Temperature  Difference  Between  Steam  in  Pipe  and  Air  Surrounding  Pipe 


50° 

100° 

150° 

200° 

250° 

300° 

350° 

400° 

450° 

500° 

Per  Cent  Efficiencies 

85.2% 

87. 

70.3% 

73.7 

72.9% 

75.9 

75.  % 
77.7 

76.8% 

79.4 

78.4% 

80.9 

80.  % 
82.4 

81.5% 

83.5 

82.9% 

84.9 

84.2% 

86. 

76.1 

78.1 

79.8 

81.3 

82.7 

84.1 

85.1 

86.3 

87.3 

88.1 

77.8 

79.7 

81.2 

82.5 

83.8 

85.1 

86.1 

87.2 

88.2 

89 

79. 

80.7 

82.3 

83.5 

84.7 

86. 

86.9 

88. 

88.8 

89.9 

81. 

82.7 

84. 

85.2 

86.2 

87.2 

88.1 

89.1 

89.9 

90.6 

82.1 

83.7 

85.1 

86.1 

87. 

88.1 

88.8 

89.8 

90.5 

91.1 

83. 

84.5 

85.7 

86.8 

87.7 

88.7 

89.4 

90.3 

91. 

91.6 

83.6 

85. 

86.2 

87.2 

88.1 

89.1 

89.8 

90.6 

91.3 

91.9 

84.2 

85.5 

86.7 

87.7 

88.5 

89.5 

90.1 

91. 

96. 

92.1 

84.6 

85.9 

87.1 

88. 

88.8 

89.8 

90,4 

91.2 

91.8 

92.3 

85. 

86.3 

87.4 

88.3 

89.1 

90. 

90.6 

91.4 

91.2 

92.5 

85.4 

86.7 

87.8 

88.6 

89.4 

90.3 

90.9 

91.7 

92.2 

92.7 

83.9 

87.1 

88.1 

89. 

89.8 

90.6 

91.2 

91.9 

92.5 

92.9 

86.2 

87.5 

88.4 

89.1 

90. 

90.8 

91.4 

92.1 

92.7 

93.1 

86  4 

87.7 

88.6 

89.3 

90.1 

90.9 

91.5 

92.2 

92.8 

93,2 

86.6 

87.8 

88.8 

89.6 

90.3 

91. 

91.6 

92.3 

92.9 

93.4 

OS 


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Page  31 

App 

. Ill 

TABLE  KO.  6 

- (CCKT’D) 

Efficiencies  of  2" 

Thick  Johns-Manville  Asbesto-Sponge  Felted  Sectional  Pipe  Insulation  on 

Various  Sizes  of  Pipe 

Temperature  Difference  Between  Steam 

in  Pipe 

and  Air  Surrounding  Pipe 

Pipe  Size, 

Inches 

50° 

100° 

150° 

200° 

250° 

300° 

350° 

400° 

450° 

500° 

Per  Cent  Efficiencies 

34  . . 

73.2% 

75.6% 

77.5% 

79.2% 

80.7% 

82.  % 

83.5% 

84.6% 

86.1% 

87.4% 

^ 

76.5 

78.6 

80.3 

81.8 

83.1 

84.2 

85.5 

86.5 

87.8 

88.8 

r ‘ 

78.8 

80.7 

82.2 

83.6 

84.8 

85.8 

87. 

87.8 

89. 

90. 

134 

80.5 

82. 

83.6 

84.9 

86. 

87.1 

88. 

88.8 

89.8 

90.8 

iH 

2 . . 

81.7 

83.4 

84.7 

85.9 

86.9 

87.8 

88.7 

89.5 

90.4 

91.2 

83.6 

85.1 

86.2 

87.2 

88.1 

89. 

89.9 

90.6 

91.4 

92.1 

2H 

3 

84.3 

86.1 

87.2 

88.2 

89. 

89.7 

90.5 

91.2 

92. 

92.7 

85.6 

86.8 

87.9 

88.8 

89.6 

90.3 

91.1 

91.7 

92.5 

93.2 

SM 

86.2 

87.4 

88.4 

89.3 

90.1 

90.8 

91.5 

92.1 

92.8 

93.5 

4 

86.7 

87.9 

88.8 

89.7 

90.5 

91.1 

91.8 

92.4 

93.1 

93.7 

4 3^ 

....  87.1 

88.3 

89.2 

90. 

90.7 

91.3 

92.1 

92.6 

93.3 

93.9 

5 ' “ 

87.5 

88.6 

89.5 

90.3 

91. 

91.6 

92.3 

92.8 

93.5 

94.1 

6 

88. 

89.1 

89.9 

90.7 

91.3 

91.9 

92.6 

93.1 

93.8 

94.3 

7 

88.4 

89.4 

90.2 

91. 

91.6 

92.2 

92.8 

93.3 

94. 

94.5 

8 

88.6 

89.6 

90.4 

91.2 

91.8 

92.4 

93. 

93.4 

94.1 

94.6 

9 

88.9 

89.9 

90.6 

91.4 

92. 

92.5 

93.1 

93.6 

94.2 

94.7 

10  

89.1 

90.1 

90.8 

91.5 

92.2 

92.7 

93.3 

93.7 

94.3 

94.8 

Efficiencies  ©/■  2^ 

" Thick  Johns- 

Manville  Asbesto-Sponge  Felted  Sectional  Pipe  Insulation  on 

Various  Sizes  of  Pipe 

Temperature  Difference  Between  Steam 

in  Pipe 

and  Air  Surrounding  Pipe 

Pipe  Size, 

Inches 

50° 

100° 

150° 

200° 

250° 

300° 

350° 

400° 

450° 

500° 

Per  Cent  Efficiencies 

34 

75.  % 

77.3% 

78.9% 

80.7% 

82.1% 

83.7% 

84.8% 

85.9% 

87.  % 

88.% 

^ 

78.2 

80. 

81.6 

83.2 

84.4 

85.7 

86.7 

87.7 

88.5 

89.3 

\' 

80.5 

82.2 

83.5 

85. 

86. 

87.2 

88.1 

89. 

89.7 

90.4 



1 Vi. 

82.2 

83.8 

84.9 

86.2 

87.2 

88.3 

89.1 

90. 

90.6 

91.3 

83.4 

84.9 

86. 

87.2 

88.1 

89.1 

89.9 

90.6 

91.2 

91.9 

2'  “ . . 

85.2 

86.5 

87.5 

88.6 

89.4 

90.3 

91. 

91.7 

92.2 

92.8 



3 

86.3 

87.5 

88.4 

89.4 

90.2 

91. 

91.7 

92.3 

92.8 

93.3 

87.1 

88.3 

89.1 

90.1 

90.8 

91.6 

92.2 

92.7 

93.2 

93.7 

3^2 

87.8 

88.9 

89.7 

90.6 

91.2 

92. 

92.6 

93.1 

93.5 

94. 

4 

88.3 

89.3 

90.1 

90.9 

91.6 

92.3 

92.9 

93.4 

93.8 

94.3 

4H 

5 

88.7 

89.7 

90.4 

91.2 

91.9 

92.6 

93.1 

93.6 

94. 

94.5 

89. 

90. 

90.7 

91.5 

92. 

92.8 

93.3 

93.8 

94.2 

94.6 

6 

89.5 

90.4 

91.1 

91.9 

92. 

93.1 

93.6 

94.1 

94.5 

94.8 

7 

89.9 

90.8 

91.4 

92.2 

92.7 

93.4 

93.8 

94.3 

94.7 

95. 

8 

90.1 

91. 

91.6 

92.4 

92.9 

93.5 

94. 

94.4 

94.8 

95.1 

9 

90.3 

91.2 

91.8 

92.5 

93.1 

93.7 

94.1 

94.6 

94.9 

95.2 

10  ...  

90.5 

91.4 

92. 

92.7 

93.2 

93.8 

94.2 

94.7 

95. 

95.3 

Efficiencies  of  3" 

Thick  Johns-Manville 

Asbesto-Sponge  Felted  Sectional 

Pipe  Insulation  on 

Various  Sizes  of  Pipe 

Temperature  Difference  Between  Steam 

in  Pipe 

and  Air  Surrounding  Pipe 

Pipe  Size, 

Inches 

50° 

100° 

150° 

200° 

250° 

300° 

350° 

400° 

450° 

500° 

Per  Cent  Efficiencies 

14 

76.8% 

78.9% 

80.6% 

82.1% 

83.4% 

84.6% 

85.8% 

87.  % 

88.1% 

89.1% 

^ . 

79.7 

81.7 

83.1 

84.5 

85.6 

86.6 

87.6 

88.6 

89.6 

90.5 

1'  ‘ 

81.9 

83.5 

84.8 

86.1 

87.1 

88. 

88.9 

89.8 

90.7 

91.5 

134 

83.5 

85. 

86.2 

87.3 

88.2 

89.1 

89.9 

90.8 

91.6 

92.3 

ri4 

84.7 

86.1 

87.2 

88.3 

89.1 

89.9 

90.6 

91.4 

92.2 

92.8 

2 ' 

86.5 

87.7 

88.7 

89.6 

90.3 

91. 

91.7 

92.4 

93.1 

93.7 

234 

87.5 

88.7 

89.6 

90.5 

91.1 

91.7 

92.4 

93. 

93.5 

94.2 

3’ 

88.4 

89.5 

90.3 

91.2 

91.7 

92.3 

92.9 

93.5 

94.1 

94.6 

3H 

89. 

90. 

90.8 

91.6 

92.1 

92.7 

93.3 

93.8 

94.4 

94.8 

4 

89.5 

90.5 

91.2 

92. 

92.5 

93. 

93.6 

94.1 

94.6 

95.1 

434 

89.9 

90.8 

91.5 

92.2 

92.8 

93.3 

93.8 

94.3 

94.8 

95.2 

5 ’ 

90.2 

91.1 

91.8 

92.5 

93. 

93.5 

94. 

94.5 

95. 

95.4 

6 

90.7 

91.5 

92.2 

92.9 

93.3 

93.8 

94.3 

94.8 

95.2 

95.6 

7 

91.1 

91.9 

92.5 

93.2 

93.6 

94.1 

94.5 

95. 

95.4 

95.8 

8 

91.3 

92.1 

92.7 

93.4 

93.8 

94.2 

94.7 

95.1 

95.5 

95.9 

9 

91.5 

92.3 

92.9 

93.5 

93.9 

94.4 

94.8 

95.2 

95.6 

96. 

10  

91.7 

92.5 

93. 

93.6 

94. 

94.5 

94.9 

95.3 

95.7 

96.1 

Pa^e  32 
App.  Ill 


TABLE  i:0.  7, 

LIST  PRICES  OF  PIPE  OOVERIEG 


SUBJECT  TO  DISCOUNT 


Standard 
Thick . . 

Thick.  . 
2"  Thick 
♦♦Double 
Standard 
Thick . . 
3"  Thick 
Broken 
Joints. . 


INSIDE  DIAMETER  OF  PIPE 


1" 

iM" 

I'A" 

2" 

2H" 

3" 

3}^" 

4" 

4M" 

5" 

6" 

7" 

8" 

9" 

10" 

12" 

*14" 

16" 

18" 

20" 

24" 

30" 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

.22 

.24 

.27 

.30 

.33 

.36 

.40 

.45 

.50 

.60 

.65 

.70 

.80 

1.00 

1.10 

1.20 

1.30 

1.85 

2.10 

2.35 

2.60 

2.85 

3.30 

4.00 

.46 

.49 

.52 

.56 

.60 

.64 

.70 

.76 

.82 

.88 

.94 

1.00 

1.10 

1.20 

1.35 

1.50 

1.65 

1.85 

2.10 

2.35 

2.60 

2.85 

3.30 

4.00 

.75 

.80 

.85 

.90 

.95 

1.00 

1.05 

1.15 

1.25 

1.35 

1.45 

1.55 

1.70 

1.85 

2.00 

2.20 

2.40 

2.70 

3.00 

3.30 

3.60 

4.00 

4.50 

5.50 

.65 

.70 

.75 

.80 

.85 

.90 

1.00 

1.10 

1.20 

1.40 

1.50 

1.60 

1.80 

2.25 

2.50 

2.70 

2.90 

4.10 

4.60 

5.10 

5.60 

6.00 

7.00 

8.40 

1.20 

1.35 

1.40 

1.45 

1.55 

1.65 

1.75 

1.90 

2.05 

2.20 

2.35 

2.50 

2.70 

2.90 

3.15 

3.40 

3.65 

4.10 

4.60 

5.10 

5.60 

6.00 

7.00 

8.40 

3^" 

H" 

1" 

IM" 

IH" 

2" 

3" 

3H" 

4" 

5" 

6" 

7" 

8" 

9" 

10" 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

$ 

Elbows  90®  & 45®.. 

.30 

.30 

.30 

.30 

.30 

.36 

.42 

.48 

.54 

.60 

.72 

.90 

1.30 

1.80 

2.40 

3.00 

3.60 

Tees 

.36 

.36 

.36 

.36 

.36 

.42 

.48 

.54 

.60 

.75 

.90 

1.20 

1.60 

2.20 

3.00 

3.80 

4.60 

Crosses 

.48 

.48 

.48 

.48 

.48 

.54 

.60 

.70 

.80 

.95 

1.10 

1.50 

2.00 

2.80 

3.60 

4.40 

5.20 

Globe  Valves 

.54 

.54 

.54 

.54 

.54 

.60 

.78 

.96 

1.20 

1.50 

1.85 

2.25 

2.80 

3.60 

4.40 

5.30 

6.20 

Flange  Covers 

.50 

.50 

.50 

.50 

.50 

.60 

.70 

.80 

.90 

1.00 

1.30 

1.60 

1.90 

2.20 

2.50 

2.90 

3.30 

These  pipe  insulations  are  supplied  in  sections  three  feet  long,  canvased  and  with  brass  lacquered  bands. 

*85%  Magnesia  is  made  in  Standard  (approx.  1").  2",  Double  Standard  Thick  and  3"  (broken  joint)  thicknesses.  For 

pipe  sizes  from  and  including  14"  in  diameter  it  is  furnished  in  segmental  form. 

Asbesto-Sponge  Felted  Insulation  is  made  in  thicknesses  from  " to  3 thicknesses  1 "and  under  use  list  prices  for  standard  thick . 

Asbestocel  and  Air-Cell  Insulations  are  made  in  M",  1",  2",  and  3"  thicknesses;  for  thicknesses  1"  and  under  use 

list  prices  for  standard  thick. 

Zero  Insulation  is  made  in  one  thickness  only,  approximately  1 Use  standard  thick  list  prices.  Prices  on  Zero  Insulation 

for  fittings  on  request. 

Anti-Sweat  Insulation  is  made  only  in  and  1"  thicknesses;  use  standard  thick  list  prices  for  all  thicknesses. 

Fittings  not  made  for  85%  Magnesia  or  Wool  Felt  Insulations. 

♦♦Applies  only  to  85%  Magnesia. 


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Page  33 
App.  IV 

APPENDIX  IV. 


TEE  FLOW  OF  STEAM  IE  PIPES. 


30  - THE  BABCOCK  FOHIULA. 

Heliable  experiinental  oata  on  the  friction  loss  of  steajE  under  various 
pressures,  and  particularly  when  superheated,  are  unfortunately  lacking. 

The  n;ost  generally  accepted  forirula  for  steam  flow  is  Babcock’s: 


P r 0,000,131  (1  + X w^  L formula  (1) 

^ D d5 

The  use  of  this  formula  may  be  greatly  facilitated  by  rearrangement  to 
the  foTOiS: 

p r w2  L V P formula  (2) 

or 

P I w^  L F formula  (3) 

D 

Nomenclature: 

p r pressure  loss,  lb,  per  sq,  in. 
w = steam  flow,  lb.  per  min. 

L r length  of  pipe  or  section,  feet, 

D = average  specific  density  of  steam,  lb,  per  cu.  ft, 

V z average  siiecific  volume  of  steam,  cu.  ft.  per  lb. 

Note:  For  superheated  steam  use  D and  V for  the  superheated 
steam  - not  the  saturated  value.  (See  calculation,  paragraph 
32). 

d r inside  diameter  of  pipe,  inches. 

P a a factor  vtoich  is  a function  of  the  pipe  diameter  only,  z 
0.000,151  ^ (see  Table  No.  8). 


Since  the  value  F is  a function  of  only  one  variable,  viz.  pipe  diam;eter, 
it  may  be  tabulated.  In  Table  No.  8 columns  1 and  4 indicate  regularlj^  manu- 
factured nominal  pipe  sizes  from  l/2  inch  upward.  Oolumns  2 and  5 show  the 
"actual”  inside  diameters  corresponding  to  columns  1 and  4,  Columns  3 and  6 
indicate  the  values  of  factor  ”F"  to  be  used  in  formulae  2 and  3 corresponding 
to  columns  1 and  4. 

31  - STA1:DABI)  and  EXTHA  STRONC  PIPES. 

It  should  be  noted  particularly  that  column  3 applies  only  to  standard 


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Page  34 
App.  IV 


TABLE  KO.  8. 

FAGTOH  FOR  THE  FCLIFIED  BABOOGK  FORl^LA. 


StiiiuUircl  Wcijcht  PijM' 

F.xlra  Heavy  Pipe 

Nominal 

Actual 

J^rt  ssuro  Lo.ss 

Nominal 

■ .-Vctual 

Prcs.sure  Loss 

Size, 

Itisulo 

Factor,  /•’ 

'^ize, 

Inskle 

Factor,  F 

Inches 

])iarn. 

Indies 

Diam. 

1 

2 

3 

4 

5 

6 

i 

0 022 

9.5.51.  X 10  ' 

5 

0 .540 

20.51 

X lO--' 

a. 

0,824 

1847. 

0 . 742 

340,8. 

10-': 

1 

1 . 049 

457 . 1 

1 

0 . 957 

777.1 

“ 

M 

1 , 380 

94  32 

li 

1 , 278 

140  7 

15 

1.610 

39.14 

15 

1 .500 

58 . 0.5 

“ 

2 

2 . 067 

9. 519 

2 

1 . 939 

13 . 05 

25 

2.409 

.3510.  x'lO  » 

25 

2.323 

4938. 

X 10-5 

3 

3 . 008 

1017. 

3 

2.900 

1432. 

35 

3 . 7)48 

■109.4 

35 

3 . 304 

029 . 5 

4 

4 . 020 

234.0 

4 

3 . 826 

310.1 

■I2 

4 . oOO 

120.9 

15 

4 . 290 

105 . 8 

n 

,■>.017 

08.54  “ 

5 

4.813 

88 . 00 

i) 

6.00.) 

2.5.44 

0 

5 .701 

33 . .5  4 

7 

7 . 023 

11.60 

7 

0 025 

1.5.84 

8 

8.071 

5.531.  X 10 -'2 

8 

7 . 025 

7482. 

X 10 

s 

7.981 

.5870. 

0 

8 . 025 

3890 . 

9 

8.941 

3210. 

10 

9 750 

2030 . 

10 

10  192 

1012 

11 

10.7.50 

1217. 

10 

10.130 

1559. 

12 

1 1 . 7.50 

704 . 1 

10 

10.020 

1703. 

13 

13.000 

450.5 

11 

1 1 . OOO 

1080. 

14 

14.000 

300  2 

12 

12.090 

0.58.2 

15 

15.000 

213.9 

12 

12.000 

084.4 

17  OD 

10  000 

153  0 

13 

13.2.50 

407.9 

18  '• 

17.000 

111.8 

14 

14.2.50 

270  2 “ 

20  ■■ 

19.000 

02 . 93 

l.j 

1.5,2.50 

190.3 

22  “ 

21 ,000 

37 . 57 

17  OI) 

16.214 

M3.0 

24  •• 

23 . 000 

23  54 

18  •' 

17.182 

105.8 

20  “ 

19.182 

.59.91 

Pa^e  35 
App.  IV 

weight  pipe,  and  column  6 to  extra  strong  pipe.  It  might  he  supposed  from  the 
nearness  of  agreement  hetv/een  the  actual  diarrieters  of  standard  and  extra  strong 
pipes  that  no  distinction  between  the  two  need  he  made  v/hen  calculating  pressure 
loss.  That  this  supposition  is  erroneous  may  he  seen  hy  comparing  columns  3 
and  6 of  the  table.  Since  the  pressure  loss  is  directly  proportional  to  factor 
”F**,  the  relative  friction  losses  in  the  tv/o  kinds  of  pipe  for  a given  nominal 
'size  may  he  observed  hy  the  ratio  of  the  two  values  of  factor  Such  a 

comparison  reveals  the  fact  that  if  column  3 he  used  for  problems  involving 
extra  strong  pipe,  the  error  would  he  -10  percent  for  12- inch  pipe,  -55  percent 
for  1/2- inch  pipe,  and  the  average  error  for  all  sizes  from  l/2-inch  to  12- inch 
inclusive  would  he  -28  percent. 

32  - SUPERHEATED  STEAl.?. 

Since  experimiental  data  on  the  flow  of  superheated  steam  are  not  available, 
it  is  necessary  to  deduce  some  relation  from  the  flov/  of  saturated  steam.. 

There  are  tv;o  conditions  which  differ  for  wet  and  superheated  steam,  viz., 
surface  condition  and  velocity.  The  difference  in  surface  condition,  is  that 
in  the  case  of  superheated  steam  the  inner  pipe  surface  is  dry,  v/hereas  in  the 
case  of  wet  steam  the  surface  is  supposedly  flushed  with  a film^  of  water. 

Several  theories  are  based  upon  this  fact.  One  is  that  the  v/ater  on  the  wetted 
surface  fills  up  the  irregularities  in  the  pipe  surface,  resulting  in  a lower 
coefficient  of  friction  for  wet  steam  than  for  dry  or  superheated  steam.. 

Another  theory,  exactly  contradictory-  to  the  foregoing,  is  that  the  moisture 
presents  a more  or  less  viscous  filament  v\hich  imposes  a drag  on  the  flov/ing 
stream  of  vapor,  and  consequently  the  coefficient  of  friction  should  he  greater 
for  wet  steam. 

The  correctness  of  either  of  these  theories  has  not  been  proved,  and  it  is 
possible  that  both  of  the  effects,  acting  in  conjunction,  counterbalance  one 
another,  resulting  in  the  same  coefficient  of  friction  for  superheated  or  dry 
steam  as  for  wet  steam/.  The  difference,  in  any  event,  is  undoubtedly  small, 
and  since  the  effect  of  velocity  is  of  considerable  magnitude,  the  effect  of 
surface  condition  may  well  be  disregarded. 

The  effect  of  the  velocity  of  flow  upon  the  pressure  loss  is  not  a simple 
one.  Friction  for  most  fluids  is  supposed  to  vary  as  the  square  of  the 
velocity,  but  a studj^  of  the  Babcock  formula  shows  that  this  relation  is  not 
universal  for  steam.  Velocity  is  affected  by:  (1)  the  weight  of  steam  flowing, 
(2)  the  cross-sectional  area  of  the  pipe,  and  (3)  the  specific  volume  of  the 
steam. 

(1)  Inspection  of  the  Babcock  formula  indicates  that  pressure  loss 
varies  as  w^  , and  since  the  velocity  is  proportional  to  w,  it  follows  that  tlie 
pressure  loss  varies  as  the  square  of  the  velocity,  which  would  be  expected. 

(2)  By  plotting  factor  ”P*  against  velocity  on  logarithmic  cross- 
section  paper,  it  is  found  that  the  friction  varies  approximately  as  the  2.6 
pov/er  of  the  velocity, or  som/evAiat  greater  than  the  square.  The  probable  ex- 
planation is  that  as  pipe  size  is  aecreased,  the  mean  hydraulic  radius  decreases, 
presenting  a compairatively  greater  frictional  surface. 

(3)  A set  of  calculations  v/ith  saturated  steam,  mahing  steam  pressure 
the  only  variable,  indicates  that  friction  varies  as  the  first  pov/er  of  the 


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Page  36 
APP«  IV 

velocity.  The  explanation  of  this  unexpected  fact  probably  lies  in  the  fact 
that  as  the  pressure  is  decreased,  although  the  specific  volume  and  hence 
velocity  are  greater,  the  density  is  correspondingly  decreasea,  and  the  number 
of  molecules  of  steam  in  contact  with  unit  surface  of  pipe  is  proportionately 
less. 

In  view  of  the  relation  found  in  the  preceding  paragraph,  it  is  the 
logical  conclusion  that,  since  the  effect  of  surface  condition  may  be  disregard- 
ed, the  friction  for  various  amounts  of  superheat  will  vary  as  the  first  power 
of  the  velocity. 

The  solution  for  pressure  loss  with  superheated  steam  may  be  made  in 
either  of  two  v/ays,  as  will  be  explained. 

(1)  Since  the  velocity  of  flow  varies  as  the  specific  volume  of  the 
steam,  either  of  the  formulae,  (l),  (2),  or  (3)  may  be  used  directly  by  merely 
substituting  the  proper  value  of  s]Decific  density  or  specific  volume  for  '*!)”  or 
”V"  respectively  from  the  superheated  steam  tables.  This  is  the  preferred 
method  when  superheated  steam  tables  are  at  hand. 

(2)  A careful  examination  of  the  properties  of  superheated  steam  indi- 
cates that  the  increase  in  volume  at  anj^  given  pressure  is  very  nearly  16  per- 
cent for  every  100  degrees  of  superheat.  This  assumption  is  so  nearly  exact 
that  the  v/orst  error  due  to  its  use  is  less  than  two  percent,  which  is  beyond 
criticism  since  there  is  four  percent  variance  between  the  experimental  co- 
efficients of  friction  as  deteimiined  by  Babcock  and  Carpenter.  The  second 
method  of  handling  superheated  steam,  then,  is  to  use  any  reliable  formula  or 
chart  designed  for  saturated  steam,  and  increase  the  pressure  loss  16  percent 
for  every  100  degrees  of  superheat, 

33  - EXAJlPhE  OF  SOLUTION  BY  THE  FORIPLA. 

Data: 

Steam  pressure  - 225  lb.  per  sq.  in,  abs. 

Superheat  - 150  deg.  F. 

Steam  Flow  - 2000  lb,  per  min. 

Pipe  - 12- inch  extra  strong. 

Determine:  Pressure  loss  per  100  feet  of  pipe. 

Solution:  Use  formula  (2) 

w r 2000  w^  s 4,000,000. 

L = 100  feet. 

V = 2,56  cu.  ft.  per  lb.  (from  steam  tables) 

F 2 764.1  X 10"^^  (from  Table  Ko.  8). 

p = 4,000,000  X 100  X 2.56  x 764.1  x lO'^^  _ 

0,782  lb,  per  sq,  in, 

34  - ORAPHIG  CHART  FOR  TEE  BABCOCK  FORJITLA. 

Although  the  solution  of  the  miOdified  formulae  is  quite  simple  v/hen  Table 
Ko,  8 and  a slide  rule  are  available,  the  logarithmic  chart.  Fig.  6,  permits  a 
quick  and  easy  solution  of  flow  problemis,  and  it  is  preferred  in  m:Ost  cases. 


< 


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Page  38 
App.  IV 

The  error  involved  in  its  use  is  not  more  than  three  percent  if  reasonable  care 
is  exercised  in  the  solution. 

This  form  of  chart  was  first  published  in  1912  by  H.  V.  Carpenter.  The 
original  chart,  hov/ever,  v/as  limited  in  its  direct  application  to  saturated 
steam  and  standard  weight  pipe,  and  the  range  of  the  quantity  of  flow  scale 
was  not  extensive  enough  for  many  modern  problems.  Pig.  6 was  drawn  by  the 
author  to  meet  these  criticisms  and  the  chart  as  presented  is  practically 
universal  in  its  application. 

35  - EXAMPLE  OF  GRAPHICAL  SOIUTION. 

The  heavy  dash  lines  on  the  chart  indicate  the  solution  of  the  same 
problem  as  solved  under  "Examiple  of  Solution  by  the  Formula".  The  solution 
is  self-explanatory  and  needs  no  further  comirient. 


T 

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